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Author Topic: multiplication easy...WHAT?!?  (Read 3937 times)

3man75

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multiplication easy...WHAT?!?
« on: March 03, 2014, 08:22:20 pm »

Okay drama aside i was wondering someone could answer this simple question. How to solve {put away your calculators dammit!} multiplication in the double digits/triple digits without using calculators. I have a online test that i doubt will let me use a calculator {although they say one or two will be provided by the test if it deems it necessary}.

Example: 23 times 45

or 156 times 471.

Basically a "paper to pen" way to multiply big numbers.
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lordcooper

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Re: multiplication easy...WHAT?!?
« Reply #1 on: March 03, 2014, 08:25:59 pm »

http://www.bbc.co.uk/schools/gcsebitesize/maths/number/multiplicationdivisionrev1.shtml

Which country doesn't teach kids this stuff before they hit double digits?
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Remuthra

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Re: multiplication easy...WHAT?!?
« Reply #2 on: March 03, 2014, 08:31:14 pm »

Basically, you break things down.

36 x 42

(6 x 2) + (30 x 2) + (6 x 40) + (30 x 40) = 12 + 60 + 240 + 1200 = 1512

Urist McScoopbeard

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Re: multiplication easy...WHAT?!?
« Reply #3 on: March 03, 2014, 08:35:51 pm »

break it down if you;re having trouble

156 x 471 = (100 x 471) + (50 x 471) + (5 x 471) + 471

              = (100 x 471) + (1/2)(100 x 471) + (1/20)(100 x 471) + 471

              = 47100 + 23550 + 2355 + 471

              = 70650 + 2355 + 471

              = 73005 + 471

              = 73476

EDIT: and just to make things fun, if f(x) = 156 * 471, then 156 * 471 = (d/dx) ∫ f(x) dx

...right?
« Last Edit: March 03, 2014, 08:40:51 pm by Urist McScoopbeard »
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Caz

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Re: multiplication easy...WHAT?!?
« Reply #4 on: March 03, 2014, 09:32:07 pm »

use boxes method. maths hax.
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Remuthra

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Re: multiplication easy...WHAT?!?
« Reply #5 on: March 03, 2014, 09:37:39 pm »

use bawkses method. maths hax.
Obligatory.

nenjin

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Re: multiplication easy...WHAT?!?
« Reply #6 on: March 03, 2014, 09:45:18 pm »

use bawkses method. maths hax.
Obligatory.

Hell, I needed this to even get multiplication as a kid. Fundamentals, yo.
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Grek

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Re: multiplication easy...WHAT?!?
« Reply #7 on: March 03, 2014, 10:14:34 pm »

23 * 45 = 45 * ( 20 + 3 ) = 900 + 135 = 1035

156 * 471 = 156 * ( 400 + 70 + 1) = 62400 + 10920 + 156  = 73476

For really tricky ones line 35351 * 53431 , use this method:
130400300050000
     1130400300050000
    50501500200001500002500000
  300300900012000090000015000000
  50005000250000200000015000000250000000
3000030000150000012000000900000001500000000

to get

Spoiler (click to show/hide)
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LordBucket

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Re: multiplication easy...WHAT?!?
« Reply #8 on: March 04, 2014, 12:16:52 am »

Quote
multiplication easy...WHAT?!?

Remember that multiplication is just addition. If you can add, then you can multiply.

Quote
23 * 45

It's easy to multiply by ten. All you have to do is add a zero. 20 is two tens.

10 * 45 = 450

Two of those is 900.

You've multiplied the 20, so all that's left is the three.  3 * 45 = 135

Add them. 900 + 135 = 1035

Using this method, pen and paper isn't required. You can do this in your head provided you learn to remember numbers you're not using.

Spoiler (click to show/hide)

Quote
156 * 471 = 156 * ( 400 + 70 + 1) = 62400 + 10920 + 156  = 73476

It's easy to multiply by 10. 150 is 15 tens. 150 is also ten tens, plus half of ten tens. So since multiplying by ten and multiples of ten is easy, think of multiplying by 150 as simply adding two zeros to the end, then adding half of the result to itself.

100 * 471 = 47100

Half of 47100 is 23550

Add them. 47100 + 23550 is 70650

Now only (6 * 471) is left to be added.

6 * 400 = 2400

Add them. 70650 + 2400 is 73050

6 * 70 = 420

Add them. 73050 + 420 = 73470

Add 6. Answer is  73476

LeoLeonardoIII

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Re: multiplication easy...WHAT?!?
« Reply #9 on: March 05, 2014, 03:45:05 pm »

Sooo I'm not seeing it described how I would describe it.

22 times 40

becomes

 22
x40



There's an extra step if we're multiplying with digits large enough to make an individual multiplication give an answer over 9.


Spoiler: Why does this work? (click to show/hide)

Spoiler: Stupid math tricks (click to show/hide)

Spoiler: Boxes (click to show/hide)
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Remuthra

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Re: multiplication easy...WHAT?!?
« Reply #10 on: March 05, 2014, 03:46:52 pm »

Sooo I'm not seeing it described how I would describe it.

22 times 40

becomes

 22
x40



There's an extra step if we're multiplying with digits large enough to make an individual multiplication give an answer over 9.


Spoiler: Why does this work? (click to show/hide)

Spoiler: Stupid math tricks (click to show/hide)

Spoiler: Boxes (click to show/hide)
That's the way I was taught originally, but it's not conducive to mental arithmetic, so I prefer to just eschew the vertical columns and such.

LeoLeonardoIII

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Re: multiplication easy...WHAT?!?
« Reply #11 on: March 05, 2014, 03:53:29 pm »

I'm sure kids get it, in schools that teach only boxes, but I suspect you need to learn some basic methods before jumping into skipping steps.
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Moogie

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Re: multiplication easy...WHAT?!?
« Reply #12 on: March 09, 2014, 07:01:31 pm »

Actually, if I were to do this in my head, I'd have broken the 3 * 45 down too. We already have 900. 2 * 45 = 90. 900 + 90 is 990. (990 + 45) = ((45 - 10) + (990 +10)) = 1035.

Took me a while to figure out why the -10 and +10 were happening. How people keep all this stuffed into their heads and still remember what question they're trying to answer, I'll never know.


Thankfully, there's no realistic real-life scenario where you wouldn't at least have a stick to scratch marks onto a surface to keep track of the numbers. If you have paper + pen, or more advanced notekeeping tech, this sort of timewasting should never be necessary. :P
« Last Edit: March 09, 2014, 07:03:58 pm by Moogie »
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Vector

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Re: multiplication easy...WHAT?!?
« Reply #13 on: March 10, 2014, 04:13:32 pm »

How people keep all this stuffed into their heads and still remember what question they're trying to answer, I'll never know.

Conservation of matter, honestly.  It helps to be a spatial thinker.
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Tiruin

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Re: multiplication easy...WHAT?!?
« Reply #14 on: March 10, 2014, 05:59:09 pm »

How people keep all this stuffed into their heads and still remember what question they're trying to answer, I'll never know.

Conservation of matter, honestly.  It helps to be a spatial thinker.
Though the problem is on what thoughts are...

On a medical note: Your brain is an enigma. Look at all those parts which are related to certain actions! They can branch into other parts if a large chunk of them are not functioning well.
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